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A091980 Recursive sequence; one more than maximum of products of pairs of previous terms with indices summing to current index. 7
1, 2, 3, 5, 7, 11, 16, 26, 36, 56, 81, 131, 183, 287, 417, 677, 937, 1457, 2107, 3407, 4759, 7463, 10843, 17603, 24373, 37913, 54838, 88688, 123892, 194300, 282310, 458330, 634350, 986390, 1426440, 2306540, 3221844, 5052452, 7340712, 11917232, 16500522 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The maximum is always obtained by taking i as the power of 2 nearest to n/2. - Anna de Mier, Mar 12 2012

a(n) is the number of (binary) max-heaps on n-1 elements from the set {0,1}. a(7) = 16: 000000, 100000, 101000, 101001, 110000, 110010, 110100, 110110, 111000, 111001, 111010, 111011, 111100, 111101, 111110, 111111. - Alois P. Heinz, Jul 09 2019

REFERENCES

A. de Mier and M. Noy, On the maximum number of cycles in outerplanar and series-parallel graphs, Graphs Combin., 28 (2012), 265-275.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..5652

A. de Mier and M. Noy, On the maximum number of cycles in outerplanar and series-parallel graphs, Elect. Notes Discr. Math 34 (2009) 489-493

Eric Weisstein's World of Mathematics, Heap

Wikipedia, Binary heap

FORMULA

a(n) = 1 + max_{i=1..n-1} a(i)*a(n-i) for n > 1, a(1) = 1.

From Alois P. Heinz, Jul 09 2019: (Start)

a(n) = Sum_{k=0..n-1} A309049(n-1,k).

a(2^(n-1)) = A003095(n). (End)

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, (g-> (f->

      1+b(f)*b(n-1-f))(min(g-1, n-g/2)))(2^ilog2(n)))

    end:

a:= n-> b(n-1):

seq(a(n), n=1..50);  # Alois P. Heinz, Jul 09 2019

MATHEMATICA

a[n_] := a[n] = 1 + Max[Table[a[i] a[n-i], {i, n-1}]]; a[1] = 1;

Array[a, 50] (* Jean-François Alcover, Apr 30 2020 *)

CROSSREFS

Cf. A003095, A056971, A309049.

Partial differences give A168542.

Sequence in context: A018057 A130137 A218022 * A274113 A005685 A141656

Adjacent sequences:  A091977 A091978 A091979 * A091981 A091982 A091983

KEYWORD

easy,nonn

AUTHOR

Franklin T. Adams-Watters, Mar 15 2004

STATUS

approved

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)